Abstract
We study and model the resonance mechanism underlying the generation of A1 and A2 screech modes in an under-expanded supersonic jet. Following our previous work [1], where upstream-travelling guided jet modes were used to provide closure of the screech resonance loop, we here consider a more complete model in which both wavenumbers and frequencies of the upstream-and downstream-travelling waves are complex. The new model requires knowledge of the upstream and downstream reflection coefficients, which are treated as parameters and identified using the experimental data. The new screech model is shown to provide a more complete description of the measured data. I. Nomenclature c ∞ = Ambient speed of sound k = Dimensionless streamwise wavenumber ω = Non-dimensional frequency m = Order of the azimuthal Fourier mode n r = Radial order of the guided jet modes St = Nozzle diameter-based Strouhal number M a = Acoustic Mach number M j = Jet Mach number U j = Jet velocity T = Jet-to-ambient temperature ratio k K H = Kelvin-Helmholtz instability mode k p = Guided jet mode L 1 = Length of the first shock cell L s = Location of the s th shock cell Re = Nozzle diameter-based Reynolds number D = Nozzle diameter r = Radial distance from the nozzle axis SPSL = Sound Pressure Spectrum Level R